Next Generation Design and Prospects for Cannex
Abstract
:1. Introduction
2. Overview Dark Sector Interactions
2.1. Dark Matter
2.2. Dark Energy
3. The Quantum Vacuum and the Casimir Effect
4. Force Metrology with Macroscopic Objects
5. New Design
5.1. Core Setup and Measurement Principle
5.2. Parallelism
5.3. Surface Flatness
- Stochastic short-scale roughness with RMS amplitude . In this limit, the actual height distribution function can be used to statistically evaluate Equation (25). While, for an actual experiment, the statistics of measured surface profiles have to be evaluated, we choose here a normal distribution around zero . The error then results from
- Large-scale deformations of the plates. For the lower plate of the recent experiment [49], the surface was measured using an optical profilometer to have a roughly spherical deformation of depth 15 nm (peak-peak) in negative direction (sag). It is technically, possible to obtain less than 10 nm sag, and the actual deformations can be measured with < nm accuracy. For the upper plate, we estimate the bend-through under gravity for a simply supported circular shell using the expression [207]Here, kg is the mass of the upper plate, , mm is the plate radius, μm is the plate thickness, and we use the values GPa and for the Young’s modulus and Poisson ratio, respectively, of silicon along the axis [205]. Equation (27) yields nm maximum bend-through at the center (). The error is then computed using Equation (25).
5.4. Vibrations and Seismic Isolation System
5.5. Thermal Errors and Control
5.6. Electrostatic Patch Effects
5.7. Detection Errors
5.8. Total Realistic Error Estimate
6. Prospects
6.1. Casimir Interactions
6.2. Dark Matter
6.3. Dark Energy
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Errors Due to Vibration
1 | |
2 | It must be noted that similar results, though mostly ignored by the Casimir community, have been obtained earlier in colloidal science, with respect to the van der Waals force being a manifestation of the same quantum effects that give rise to Casimir forces. |
3 | The real and imaginary parts of the complex dielectric susceptibilities are usually denoted as with a similar notation for the complex magnetic susceptibilities. |
4 | The appearance of complex functions results from the infinite integration of the mode density functions over real frequencies. As the latter have poles, the integration contour splits into a half-circle at infinity and an integration from to + . The former term vanishes due to for , leaving the integration over the complex frequency axis. |
5 | Note that, for graphene, the thermal contribution to the Casimir effect is significant at much smaller separations [178]. However, this effect could not be measured yet. |
6 | Note that the actual quantity measured in torsion pendula experiments is a torque. For the purpose of comparing the order-of-magnitude sensitivity of Ref. [32] to other experiments with force detection, we divide the torque sensitivity fNm by the effective radius of the test mass. For comparing the pressure (again only as rough estimation), we assume the entire torque-generating area of 10 2 to contribute homogeneously. |
7 | This form of connection is similar to a jewel bearing. Further contact is made via the three glass fibers having low thermal conductance ∼ W/m K [217] and three thin wires establishing electrical contact that, however, are thermalized via the Peltier element. |
8 | Here, we preclude that any hypothetical force will be much smaller than the Casimir force, as the latter has been measured at the percent level without significant disturbance. However, we may not a priori exclude the possibility that a hypothetical additional force may be responsible for the discrepancy between data and predictions by Lifshitz theory with the Drude model discussed in Section 6.1. |
9 | Note that, due to time constraints during manuscript preparation, we show in Figure 10 only and calculated using the Drude model, rather than the plasma model. |
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Experiment, | Object | Force Gen. | Sensitivities | ||
---|---|---|---|---|---|
Geometry | Size | Area | Force | Pressure | Ref. |
[cm] | [pN] | [pN/cm] | |||
interfacial measurements | |||||
AFM-type, sphere/plane | 100 μm | [200] | |||
torsional balance, sphere/sphere | 10 cm | [35] | |||
micro-oscillator, sphere/plane | 100 μm | [164] | |||
prospective | |||||
Cannex oscillator, plane/plane | 1 cm | [50] | |||
Cavendish-type measurements | |||||
micro-cantilever, cube/plane | 100 μm | [27] | |||
torsion balance, patterned plates | 10 cm | [32] |
Parameter | Value | Error | Unit | Main Error Source |
---|---|---|---|---|
Sensor mass | 31.748 | 0.003 | mg | Vibrations and phase noise during calibration |
Sensor area A | 1.0834 | 0.0005 | cm | Measurement uncertainty |
Sensor extension | variable | 0.1 | pm | Laser linewidth, electronic noise. |
Sensor free resonance | 10.243 | Hz | Lower IF linewidth, electronic noise. | |
Sensor quality factor Q | - | 1 | Residual gas | |
Upper IF wavelength | 1590.0 | nm | Laser stability | |
Upper IF linewidth | 15 | - | kHz | - |
Upper IF detector noise (RMS) | 1 | - | - | |
Lower IF wavelength | 1550.0 | nm | Laser stability | |
Lower IF linewidth | 10 | - | MHz | - |
Lower IF detector noise (RMS) | 100 | - | - | |
PLL frequency resolution | 1 | - | - | |
PLL phase noise (RMS) | 1 | - | - | |
Excitation voltage ampl. | mV | Measurement uncertainty | ||
Voltage feedback ampl. | mV | Measurement uncertainty | ||
Effective sensor vibr. ampl. (RMS, s) | 0.106 | - | pm | Measurement uncertainty |
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Sedmik, R.I.P.; Pitschmann, M. Next Generation Design and Prospects for Cannex. Universe 2021, 7, 234. https://doi.org/10.3390/universe7070234
Sedmik RIP, Pitschmann M. Next Generation Design and Prospects for Cannex. Universe. 2021; 7(7):234. https://doi.org/10.3390/universe7070234
Chicago/Turabian StyleSedmik, René I. P., and Mario Pitschmann. 2021. "Next Generation Design and Prospects for Cannex" Universe 7, no. 7: 234. https://doi.org/10.3390/universe7070234